How To Find The Square Root Of 7? - Cuemath

Square Root of 7

The square root of 7 is expressed as √7 in the radical form and as (7)½ or (7)0.5 in the exponent form. The square root of 7 rounded up to 8 decimal places is 2.64575131. It is the positive solution of the equation x2 = 7.

• Square Root of 7: 2.6457513110645907
• Square Root of 7 in exponential form: (7)½ or (7)0.5
• Square Root of 7 in radical form: √7

Let's explore more about finding the square root of 7 in this mini-lesson.

1.	What Is the Square Root of 7?
2.	Is Square Root of 7 Rational or Irrational?
3.	How to Find the Square Root of 7?
4.	Important Notes on Square Root of 7
5.	Tips and Tricks
6.	FAQs on Square Root of 7

What Is the Square Root of 7?

• The square root of a number is the number that when multiplied to itself gives the original number as the product.
• √7 = 2.645 x 2.645 or -2.645 x -2.645

Is the Square Root of 7 Rational or Irrational?

• A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0.
• √7  = 2.645751311064591. Due to its never-ending nature after the decimal point, √7 is irrational.

How to Find the Square Root of 7?

The square root of 7 can be calculated using the average method or the long division method. √7 cannot be simplified any further as it is prime. The radical form of the square root of 7 is √7.

Square Root of 7 by Average Method

• The square root of 7 will lie between the square root of the two perfect squares closer to 7.
• We will first identify the square root of 4 and the square root of 9. √4 < √7 < √9.
• Thus, we determine that the square root of 7 lies between 2 and 3. 2 < √7 < 3
• Using the average method, find 7 ÷ 3 or 7 ÷ 2.
• 7 ÷ 3 = 2.33
• Find the average of this quotient obtained and 3. Average = (2.33 + 3) ÷ 2 = 5.33 ÷ 2 = 2.66
• Thus, √7 = 2.66 by the average method.

Square Root of 7 by Long Division Method  

• Write 7 as 7.000000. Consider the number in pairs from the right. So 7 stands alone.
• Now divide 7 with a number such that number × number gives 7 or a number lesser than that. We determine 2 × 2 = 4
• Complete the division process. Obtain 2 as the quotient and 3 as the remainder. Bring down the first pair of zeros.
• Double the quotient obtained. Now 2 × 2 forms the new divisor in the tens place.
• Find a number which in the units place along with 40, fetches the product 300 or a number lesser than that.
• We find that 6 × 46 gives 276. Complete the division and get the remainder as 24.
• Now our quotient is 2.6. Double this and get 520 as our new divisor.
• Bring down the next pair of zeros. Find the number that with 520 gives 2400 or a number lesser than that.
• We conclude 4 × 524 = 2096. Complete the division.
• Repeat the same division process until we get the quotient approximated to 3 digits.
• Thus, we have evaluated √7 = 2.645.

Explore square roots using illustrations and interactive examples.

• Square root of 5
• Square root of 8
• Square root of 9 
• Square root of 12
• Square root of 2

Important Notes

• The square root of 7 is expressed as √7 in the radical form and as 7½ in the exponential form.
• The square root of a number is both negative and positive for the same numerical value, i.e., the square root of 7 is +2.645 or -2.645.

Tips and Tricks

• The square root of 7 lies between the perfect squares closer to 7. Thus, √7 lies between 2 and 3.
• Use the average method to determine the approximate value of 7 and the division method to determine the accurate value of √7.